High Resolution Spatio-Temporal Model for Room-Level Airborne Pandemic Spread Teddy Lazebnik1and Ariel Alexi2

2025-05-06 0 0 1.41MB 26 页 10玖币

侵权投诉

High Resolution Spatio-Temporal Model for Room-Level Airborne

Pandemic Spread

Teddy Lazebnik∗†1and Ariel Alexi∗2

1Department of Cancer Biology, Cancer Institute, University College London, London, UK

2Department of Information Science, Bar-Ilan University, Ramat-Gan, Israel

October 10, 2022

Abstract

Airborne pandemics have caused millions of deaths worldwide, large-scale economic losses, and catas-

trophic sociological shifts in human history. Researchers have developed multiple mathematical models and

computational frameworks to investigate and predict the pandemic spread on various levels and scales such as

countries, cities, large social events, and even buildings. However, modeling attempts of airborne pandemic

dynamics on the smallest scale, a single room, have been mostly neglected. As time indoors increases due to

global urbanization processes, more infections occur in shared rooms. In this study, a high-resolution spatio-

temporal epidemiological model with air ﬂow dynamics to evaluate airborne pandemic spread is proposed.

The model is implemented using a high resolution 3D data obtained using a light detection and ranging

(LiDAR) device and computing the model based on the Computational Fluid Dynamics (CFD) model for

the air ﬂow and the Susceptible-Exposed-Infected (SEI) model for the epidemiological dynamics. The pan-

demic spread is evaluated in four types of rooms, showing signiﬁcant diﬀerences even for a short exposure

duration. We show that the room’s topology and individual distribution in the room deﬁne the ability of air

ventilation to reduce pandemic spread throughout breathing zone infection. keywords: Agent-based sim-

ulation, Indoor pandemic, Airborne pathogens, Mask-wearing intervention policy, SEI model, Indoor CFD

simulation.

1 Introduction

Humanity suﬀered multiple pandemics during its history [1]. In just the last few hundred years, pandemics

caused signiﬁcant mortality, economical crises, and political shifts [2]. For example, tens of millions of individuals

worldwide died due to the 1918 inﬂuenza pandemic [2]. Another example is the coronavirus (COVID-19)

∗These authors contributed equally.

†Corresponding author: t.lazebnik@ucl.ac.uk

arXiv:2210.03431v1 [cs.IR] 7 Oct 2022

pandemic which was declared by the World Health Organization (WHO) as a public health emergency of

international concern in 2020 and resulted in around six million deaths over the ﬁrst two years [3, 4].

As such, policymakers are faced with the challenge of controlling a pandemic spread. In particular, this

challenge becoming increasingly more relevant, as urbanization grows in the developing world is bringing more

people into denser neighborhoods, which results in a higher infection rate, at which new diseases are spread

[5]. Indeed, Wu et al. (2017) have shown that the overall globalization processes taking place in the recent few

decades have facilitated pandemic spread [6]. These and other social and economic processes are predicted to

make the infectious disease outbreaks nearly constant in the near future [1].

Pandemics are taking many shapes such as sexual transmitted diseases (for example, HIV) [7, 8], social

inﬂuenced behavior (like, alcoholism) [9, 10], and airborne diseases (such as inﬂuenza) [11, 12]. The group

of airborne pandemics are including viruses such as the Lassa virus, Nipah virus or poxviruses, COVID-19,

inﬂuenza, and others. These are a cause for concern owing to their infection rate and potential for global spread

[13]. Consequently, pandemic intervention policies (PIPs) for airborne pandemics are known to be relatively

more harmful to the economy and psychological state of the population relative to other types of pandemic

[14, 15, 16, 17, 18].

Multiple models have been proposed to describe airborne pandemics [19, 20], mostly extending the Susceptible-

Infected-Recovered (SIR) model proposed by [21]. More often than not, these models are working well for large

population sizes and relatively long period of time, providing a ﬁne prediction of the pandemic spread and the

inﬂuence of a wide range of PIPs on average. However, since these models are focusing on large populations

and usually large-scale spatial locations such as cities and countries, they provide less accurate predictions for

small size populations in small spatial locations which mainly left neglected.

In this work, we propose a high-resolution spatio-temporal epidemiological model for a case of a single room

with a small population. The model is inspired by the SIR model and takes into consideration three-dimensional

spatial dynamics with air ﬂow. In particular, individuals are infected by breathing pathogen particles from the

air and infect others by breathing out pathogen particles. Using the proposed model, one is able to better

approximate the airborne pandemic spread in small populations located in a room. The novelty of the proposed

model lies in the integration of a computational ﬂuid dynamics simulator for air ﬂow with a spatio-temporal

epidemiological model and focusing on a small size population over a short duration.

The proposed model is evaluated for four types of rooms (classroom, conference room, movie theater, and

restaurants), reviling statistically diﬀerent pandemic spread dynamics. In addition, the inﬂuence of the mask-

wearing and artiﬁcial air ventilation (AAV) PIPs are evaluated for each room type on a wide range of possible

conﬁgurations. The mask-wearing is shown to better reduce the pandemic spread compared to AAV for all

room types. We ﬁnd that the distribution of individuals in the room has a major inﬂuence on the eﬃciency of

AAV, mainly depending on the amount of breathing zone infections.

The paper is organized as follows. Section 2 outlines the current epidemiological and air movement models

and their simulations approaches. Section 3 introduces the proposed mathematical model with computer simu-

lation. Section 4 presents several simulations based on the proposed model. In Sections 5 and 6, we discuss the

results and oﬀer future work.

2 Background

Multiple studies show that mathematical models and computer simulations are powerful tools for policymakers

to investigate pandemic spread and diﬀerent PIPs with their outcomes in a fast, cheap, and controlled manner

[20, 19, 22]. There are multiple modeling approaches for epidemiological dynamics [23, 24, 25]. The leading

approach is extending the SIR model [21] with sociological [20], economic [26], biological [19], and clinical [27]

dynamics to name a few.

More often than not, these models obtain relatively poor results for medium and long prediction periods.

One explanation for this shortcoming is the assumption that the population is well mixed which known to be

false even for small population sizes and spatial locations [28, 29, 30, 31, 32, 33]. Indeed, Cooper et al. (2020)

used the SIR model on the COVID-19 pandemic while relaxing the assumption that the population is mixing

homogeneously, showing a fair ﬁtting on six countries with improved results compared to the classical SIR model

[34]. In general, long time periods is hard to predict simply due to statistical ﬂuctuations.

To tackle this challenge, several models introduced spatial dynamics to the spread of a pandemic which can be

divided into two main groups: graph-based and metric space. Graph-based models take an abstract approach

to modeling the locations in which individuals can be located at. Usually, it is assumed that each node in

the spatial graph represents a physical location (such as a room, street, city, or even a country) and that the

population is well-mixed in each node [22, 30]. This approach more often than not ignores the physical properties

and dynamics that occur in the location represented by the graph’s nodes. For instance, Lazebnik et al. (2021b)

proposed a two age-group extended SIR model with a three-node graph representing a school, a home, and a

work such that the individuals move between them according to their age group and time of the day [35]. Moore

and Newman (2000) study several models of disease transmission on small-world networks, in which either the

probability of infection by a disease or the probability of its transmission is varied, or both [36]. The authors

conducted a numerical analysis which results present a similar behavior to the reported data by [29]. Klovdahl et

al. (1994) deﬁned and explored the stochastic SIR model on a graph of interactions to represent the pandemic in

a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale [31].

The authors used real data on trade-related cattle movements from a densely populated livestock farming region

in western France and epidemiological parameters corresponding to an infectious epizootic disease, obtaining

fair prediction accuracy. Additionally, Lazebnik and Alexi (2022) proposed a graph-based extended SIR model

where each node represents a room in a building [28]. The authors examined the inﬂuence of the diﬀerent

moving patterns of the population in several building types (home, school, oﬃce, and mall) on the pandemic

spread and on the optimal conﬁguration of both spatial and temporal such as mask-wearing and vaccination,

respectively. Nevertheless, the authors assumed that the population is well-mixed in each room. As a result,

their model produced noisy results for the case of the home-type building, where the population density is low.

On other hand, for the case of spatial models, it is assumed that the space is continuous and people move in

the space over time, representing a more physically accurate representation of movement. For instance, Milner

and Zhao (2008) proposed a SIR based model where susceptible individuals move away from the previous

location of the infection, and all individuals move away from overcrowded regions [37]. Fabricius and Maltz

(2020) developed a stochastic SIR model with global and local infective contacts [38]. Paeng and Lee (2017)

proposed a SIR based model where individuals are assumed to move stochastically within a small ﬁxed radius

rather than a random walk [39]. The authors proposed continuous and discrete SIR based models that show

spatial distributions. They show that the propagation speed and size of an epidemic depend on the population

density and the infectious radius.

In the context of airborne pandemics, one can focus on the infection that occurs in a room by tracking the

air ﬂow with the pathogen particles it carries between the individuals in the room [40]. Wei and Li (2016) review

the release, transport, and exposure of expiratory droplets because of respiratory activities in the context of a

pandemic indoor [41]. The authors concluded that droplets or droplet nuclei are transported by air ﬂow, which

is sometimes aﬀected by the human body plume. They suggested that the usage of a face mask, as well as room

air ventilation, can reduce the infection rate.

Air ﬂow (or air movement) dynamics are vastly explored in multiple contexts such as healthcare [42], me-

chanics [43], agriculture [44], and epidemiology [40]. In particular, Peng et al. (2020) explored the pandemic

spread of the airborne COVID-19 pathogen in indoor settings using a combination of the box and Wells-Riley

models [45, 46]. The authors have derived an expression for the number of secondary infections. Nonetheless,

their model is not taking into consideration a detailed, and accurate representation of the room’s geometry.

Moreover, the box model used by the authors does not correctly represent common cases such as rooms where

clear directional ﬂow or infection due to overlapping breathing zones. In this work, we aim to tackle these

challenges using more detailed air ﬂow dynamics.

There are various modeling approaches to predict the air ﬂow within buildings such as Multi-zone models

and Zonal models. However, Computational Fluid Dynamics (CFD) models considered to be the most accurate

for a single room [47, 48].

The CFD models are numerical methods of solving ﬂuid ﬂow using the Navier-Stokes (NS) equations [49].

These models use numerical algorithms to integrate the NS equations over a given mesh by converting the integral

equations to algebraic equations (e.g., discretization) and then solving them iteratively [50]. In the context of

building air ﬂow or even room-level air ﬂow, the CFD modeling approach subdivides an individual room into

many space segments and each one is treated as an atomic segment in which the NS equations are computed

[47]. There are three main types of CFD implementation for indoor air ﬂow dynamics: Reynolds-Averaged

Navier-Stokes (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS) [51].

The RANS equations take advantage of the Reynolds decomposition technique whereby an instantaneous

quantity is decomposed into ﬂuctuating quantities and the average value of some time duration. This technique

provides approximations over time of the NS equations, averaging the results on short periods [52]. Comple-

mentary, DNS numerically solves full Navier–Stokes equations using a very ﬁne mesh to capture all the scales

that are present in a given ﬂow. Interrelate, LES computes large-scale motions similarly to DNS but with a

larger grid, and sub-grid scale dynamics are solved using an averaging method such as the RANS approach.

While all three CFD computational approaches are able to provide accurate predictions for air ﬂow, the RANS

approach is the most popular one for the indoor environment. This is because the other two CFD approaches

are signiﬁcantly more computationally expensive without a justiﬁed improvement in prediction accuracy for

most cases [53].

Several CFD-based models and simulators have been developed for indoor context [54, 55, 56]. Hiyama and

Kato [54] developed a 3D CFD model for close space with air ﬂow in whole building settings. The authors

integrated the outcomes of the CFD simulation with building energy simulations to achieve a more accurate

time-series analysis of building energy consumption compared to conventional energy simulations [54]. Nahor

et al. [55] proposed a 3D CFD model to calculate the velocity, temperature, and moisture distribution in an

existing empty and loaded cool store. The authors validated their model with data from several experiments

and show that the model was capable of predicting both the air and product temperature with reasonable

accuracy [55]. Smale et al. [56] reviewed the application of CFD and other numerical modeling techniques

to the prediction of air ﬂow in refrigerated food applications including cool stores, transport equipment, and

retail display cabinets. The authors show that given enough computation power, CFD-based models obtain

high accuracy in all these tasks. For the case of an individual breathing in a room, Cravero and Marsano shown

that the CFD model provides a ﬁne accuracy to the air movement including breathing dynamics, air ventilation,

and air diﬀusion [57]. Thusly, CFD-based models are accurately describing the air movement dynamics across

a wide range of environments in general and room types in particular. As such, the CFD model implemented

using the RANS method is used in this research.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

HighResolutionSpatio-TemporalModelforRoom-LevelAirbornePandemicSpreadTeddyLazebnik*1andArielAlexi21DepartmentofCancerBiology,CancerInstitute,UniversityCollegeLondon,London,UK2DepartmentofInformationScience,Bar-IlanUniversity,Ramat-Gan,IsraelOctober10,2022AbstractAirbornepandemicshavecausedmillions...

展开>> 收起<<

High Resolution Spatio-Temporal Model for Room-Level Airborne Pandemic Spread Teddy Lazebnik1and Ariel Alexi2.pdf

共26页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

High Resolution Spatio-Temporal Model for Room-Level Airborne Pandemic Spread Teddy Lazebnik1and Ariel Alexi2

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: